Analysis of a Delayed Delta Modulator.

Delayed Delta Modulation DDM uses a second feedback loop in addition to the standard DM loop. While the standard loop compares the current predictive estimate of the input to the current sample, the new loop compares it to the upcoming sample so as to detect and anticipate slope overloading. Since this future sample must be available before the present output is determined and the estimate updated, delay is introduced at the encoding. The performance of DDM with perfect integration and step-function reconstruction is analyzed for each of three inputs. In every case, the stochastic stability of the system is established. For a discrete time i.i.d input, the limiting joint distribution of input and output is derived, and the asymptotic mean square sample point error MSESP is computed when the input is Gaussian. For a Wiener input, the joint distribution of the sample point and predictive errors is derived, and MSESP and the time-averaged MSE MSETA are computed. For a stationary, first-order Gauss-Markov input, the joint distribution of input and output is derived, and MSESP and MSETA computed. Graphs of the MSEs illustrate the improvement attainable by using DDM instead of DM. With optimal setting of parameters, MSESP MSETA is reduced about 15 35. Author